Warm-Up #34 Thursday, 12/10

Homework Thursday, 12/10 Lesson 4.02 packet Pg____________________

Warm-Up #35 Friday, 12/11

Homework, Friday 12/11 Lesson 4.03 packet Pg 2 and

Lesson 4.02_Explicit and Recursive Form

Arithmetic Sequence It is a sequence that goes from one term to the next term by always adding or subtracting to the same value Example:

Common difference (notation= d) It is the difference between each number in an arithmetic sequence

Geometric Sequence It is a sequence that goes from one term to the next by always multiplying or dividing by the same value Example:

Common ratio (notation = r) It is the ratio of a term to the previous term in a geometric sequence.

Sequence A sequence always start with the 1 st term. Example: {3, 5, 7, 9…} So what is the 0 th term for this example? Explain. 1 st term 2 nd term

Practice Problems 1){24, 27, 30, …} 2)(56, 66, 76, …} 3){4, 16, 64…} 4){50, 25, 12.5, …}

Arithmetic Sequence If the sequence is an arithmetic sequence, then it is a linear function with an equation of y = mx + b

Geometric Sequence

5-Minute Check 1 A.arithmetic B.geometric C.neither Which best describes the sequence 1, 4, 9, 16, …?

5-Minute Check 2 A.arithmetic B.geometric C.neither Which best describes the sequence 3, 7, 11, 15, …?

5-Minute Check 3 A.arithmetic B.geometric C.neither Which best describes the sequence 1, –2, 4, –8, …?

5-Minute Check 4 A.–50, 250, –1250 B.–20, 100, –40 C.–250, 1250, –6250 D.–250, 500, –1000 Find the next three terms in the geometric sequence 2, –10, 50, ….

known values Explicit Formulas

What is a recursive sequence? Definition: A recursive sequence is the process in which each step of a pattern is dependent on the step or steps before it.

Recursion Formulas “Rate of change”

Sequence and Terms Let’s look at the following sequence 1,4,9,16,25,36,49,…, The letter a with a subscript is used to represent function values of a sequence. The subscripts identify the location of a term. Do you know what the rule is for the sequence? n²

How to read the subscripts: a term in the sequence the prior term the next term

Ex. 1: Find the first four terms of the sequence: The first term is 5 Each term after the first + 2 is 3 times the previous term Plus 2 Let’s be sure we understand what is given General Term

Continued… Ex. 1: Find the first four terms of the sequence: n=1 n=3 n=2 n=4 given Start with general term for n>1 Answer = 5, 17, 53, 161

Your turn: Ex 2: Find the next four terms of the sequence. given Start with general term for n>1 Answer = 3, 6, 12, 24 n=1 n=3 n=2 n=4

Try another… n=1 n=3 n=2 n=4 given = = 4 – 4 = 0 0 – 2 = -2 Answer = 2, 1, 0, -2, -8 n=5 = -8 – 0 = -8 given

Your turn Write a recursive formula for the sequences below. Step 1 : Determine if it is arithmetic or geometric. Step 2 : Plug in to either the geometric or arithmetic recursive formula. Step 3 : Make sure you tell us what a 1 is equal to. Ex. 3 7, 3, -1, -5, -9, … The common difference = -4 The first term = 7 Ex. 4 3, 6, 12, 24, 48, … The common ratio = 2 The first term = 3

The first row of the theater has 15 seats in it. Each subsequent row has 3 more seats that the previous row. If the last row has 78 seats, how many rows are in the theater? Example